The study programme is primarily intended for prospective researchers, professors and other academic staff. Each student has a supervisor, who is ordinarily selected before the student’s enrolment. One of the key roles of the supervisor is to present a relevant open problem (or open problems) to the student. While the student is trying to solve the problem (or problems), the supervisor helps, informs the student of similar problems already solved and introduces appropriate techniques from relevant mathematical fields. The solution to these open problems and its publication in the relevant international journals must be a primary goal of each student.

In the first year, there are two elective courses - Advanced Mathematical Course I and Advanced Mathematical Course II. Their purpose is to acquaint students with topics with which they did not become familiar during lower-level studies, but which are indispensable for research in their field. Courses are often suggested by the supervisor and are usually individual to the student. Students regularly present their current research work at research seminars.

The aim of the programme is to encourage students to do the research, and not to burden them with course exams that are not directly related to their research area (the latter is probably a special feature among Slovenian universities). Faculty members are aware of the fact that nowadays Ph.D. students must have some research results immediately after finishing their studies if they want to stay in academia – whether that be abroad or at home.

During their studies, Ph.D. students usually attend various international conferences and conduct research visits, where they present their research results. Often they are involved in the organization of the conferences, summer schools, etc., organized by the Faculty or UP IAM, which is directly connected with the faculty. To a lesser extent, students are also involved in teaching students at lower levels.

Educational and professional goals

After (or during) the study programme, the student is capable of independent, internationally competitive research work.

The student publishes articles in reputable international journals listed on the Science Citation Index Expanded. This is also a prerequisite for a successful dissertation defence.

The student knows his/her research area thoroughly, having the latest information on open problems or the problems that have already been solved.

During the study programme, the student becomes familiar with the career of a researcher (active participation in international conferences, research visits, etc.).

The doctoral degree study is provided on an individual basis. The main components of the study programme are the following:

Advanced mathematical courses covering the research topic chosen by the candidate together with the supervisor

Research by the candidate

Seminar presentations

A minimum of two scientific articles in SCI journals

Doctoral dissertation and defence

All these activities must add up to 180 ECTS.

Advanced Mathematical Courses (AMC I and AMC II) are the basis of the doctoral student’s Individual Research work and introduce the candidate to problems associated with each of the following fields of Mathematics: Analysis, Algebra, Discrete Mathematics, Financial Mathematics, Cryptography, Computing Intensive Methods Applications, and Statistics.

Students select a supervisor with research interests similar to their own, who mentors their chosen AMC I or AMC II courses and doctoral dissertation. The choice of courses is usually made in consultation with the student’s supervisor. Similar study programmes, within the field of natural sciences, either inside or outside the university, may also be chosen. The University of Primorska provides one such option within their Information Technologies Doctoral programme.

In studying these courses, with the benefit of their supervisor’s input and direction, students acquire the necessary skills to enable them to perform individual research work in any of the above-mentioned fields of Mathematics. Candidates' Individual Research work is shared with their supervisor during their consultations; it is also introduced to teachers, students and others during seminars and concluded by their doctoral dissertation.

A doctoral dissertation represents an original contribution to science and, consequently, has to conform to University rules and regulations on doctoral dissertations.

As part of their studies, students are required to write a doctoral dissertation, which must represent a new and important contribution to the body of knowledge in the field of mathematics. Prior to the thesis defence (viva voce), their research must be published (or accepted for publication) in international journals in the field of mathematics, in at least two articles in journals from the SCI list. Detailed criteria are established by the Department of Mathematics of UP FAMNIT.

A Master's degree in studies similar to Mathematics (Computer and Information Sciences, Information Science and Mathematics, Natural Sciences) who have met the necessary additional requirements (i.e. passed differential exams in Algebra and Analysis).

In the case of enrolment limitations, applicants shall be selected on the basis of their performance demonstrated in Master's studies (average grade, Master’s thesis grade).

Admission may also be gained by an applicant having completed a comparable study abroad. Prior to enrolment the applicant must apply for recognition of completed education.

Transfers between study programmes are possible on the basis of the Higher Education Act, Criteria for Transferring between Study Programmes and in accordance with other provisions regulating this field.

Transferring between study programmes means a cessation of studies in the first study programme and the continuation of studies in the second study programme. The first study programme is the programme from which the student is transferring. The second study programme is the programme to which the student is transferring. Applications for transfers shall be considered on the grounds of the level of comparability between study programmes and those study requirements which students have already completed in their first study programme.

Entry into Year 2 or Year 3 of the doctoral degree programme of Mathematical Sciences on the basis of the Criteria for Transferring between Study Programmes is open to students of a related third-cycle doctoral degree programme or a pre-reform Master’s programme (adopted prior to 11 June 2004), provided that the following conditions have been met:

the student fulfils the requirements for admission to the study programme of Mathematical Sciences;

completion of the first study programme which the student is transferring from ensures the acquisition of comparable competencies as those envisaged by the study programme of Mathematical Sciences; and

other conditions in accordance with the Criteria for Transferring between Study Programmes have also been met (a comparable course structure, course requirements completed).

Entry into Year 2 of the doctoral degree programme of Mathematical Sciences on the basis of the Criteria for Transferring between Study Programmes is also open to graduates of a related Master’s degree programme adopted before 11 June 2004.

Individual applications for transfer shall be considered by the relevant committee of UP FAMNIT. Apart from comparability between both fields of study, the committee shall also consider comparability between the study programmes, in accordance with the Criteria for Transferring between Study Programmes.The applicant may also be required to complete differential exams as defined by the relevant Faculty committee.

Enrolment on the basis of the Criteria for Transferring between Study Programmes is also open to students of a related study programme abroad who have been, in the process of recognition of their studies abroad, legally granted the right to continue their educational training in the study programme of Mathematical Sciences.

In the case of limited enrolment, applicants shall be selected on the basis of the average grade obtained during the study programme they are transferring from.

In the 1st year, students complete two courses within the cluster of in-depth mathematical contents which they select in consultation with their supervisor.

The two courses above provide the basis for individual research work (2nd and 3rd year) on which students are to report to their supervisor. Individual research work is presented at department seminars attended by students, teachers and other interested persons. The contents of the seminars (two each year) relate to the above-mentioned courses from the cluster in-depth mathematical contents. Individual research work is completed through the preparation of the Doctoral dissertation, presenting an authentic contribution to science.

Prior to the thesis defence (viva voce), the student's research must be published (or accepted for publication) in international journals in the field of mathematics, in at least two articles in journals from the SCI list. Detailed criteria are established by the Department of Mathematics of UP FAMNIT.

Graduates are equipped for either independent research or other development projects demanding exacting knowledge, at the national or international level, and are also capable of working on university projects, in scientific institutes or in other research and development organisations. The in-depth knowledge acquired in both theoretical and applied mathematics also enables graduates to seek employment outside the academic environment, i.e. in insurance companies, banks, stockbroking agencies, statistical offices, and in economic environments where the need for survival and development in competitive market economies requires people capable of rational thinking, in-depth analysis and substantial decision making skills - in short, mathematicians.